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Design of Headed Anchor Bolts
OHN G. SHIPP AND EDWARD R. HANINGER
n current practice the design of base plates is controlled by
earing restrictions on the concrete (see Fig. 1); shear is
ransmitted to the concrete largely through anchor bolts,hear lugs or bars attached to the base plate and the tensile
nchorage steel is generally proportioned only for direct
tress. The embedment requirements for anchorage steel are
ot clearly defined by most codes and are left largely to the
iscretion of the design engineer. Also, there are no
rovisions to prevent a brittle failure in the concrete as
pposed to a ductile failure in the anchor bolt, as provided
or with a probability-based limit states design or Load and
Resistance Factor Design (LRFD) for steel.8 Larger design
orces now mandated in many areas due to the revised
eismic and wind loads require design capacities for anchor
olts beyond any existing code values.6,11
Therefore, there isneed for a complete design procedure for anchor bolts that
will accommodate these larger loads and incorporate the
roposed design philosophy, i.e., probability-based limit
tates design (PBLSD).8
THE HEADED BOLT AS AN ANCHORAGE
The headed bolt,as designed herein, is recommended as the
most efficient type of anchorage to use for both tension and
hear loads. Other anchorages which have been used are L-
olts, J-bolts, rods with a bolted bearing plate and shear lugs.
L-bolts have been shown to be less effective in resisting slip
t service load levels than headed bolts.13The authors are not
ware of any published data that addresses the performance
f J-bolts. For a threaded rod with a bolted washer or bearing
late embedded in concrete, tests have shown that unless the
late is properly sized it may actually decrease the anchor
apacity by causing a weakened failure plane in the
oncrete.7,17
Shear lugs can fail in a brittle mode if not
roperly confined, and do not lend themselves to a shear
riction analysis.7,17
The headed bolt, when properly embedded and confined,
will develop the full tensile capacity of even A490 high
ohn G. Shipp is Supervising Structural Engineer, Fluor Engineersand Constructors, Inc., Irvine, California.
Edward R. Haninger is Senior Structural Engineer, Fluor Engineers
and Constructors, Inc., Irvine, California.
strength bolts.3 When the tension capacity of the bo
developed, a ductile failure can be ensured by the s
friction mechanism.3
In this paper, anchor bolt design ductility is assure
causing a failure mechanism that is controlled by yieldin
the anchor bolt steel, rather than brittle tensile failur
concrete. This is accomplished by designing the pu
strength of the concrete failure cone (Up) such th
equals the minimum specified tensile strength (FuAt) or
anchorage value of the anchor bolt. See Figs. 2 and 10
illustrations of the concrete failure cone concept.
Appendix A for the derivation of Ld to satisfy this crit
The design approach presented herein is compatible with
proposed AISC Specification for Nuclear Facilities,5
318-77,2
and the proposed revisions to ACI 318-77.7
governing design approach is that presented in ACI
Supplement 1979.3
DESIGN PARAMETERS
The design approach presented is generally applicable to
of a number of bolt or concrete strengths. However,
following representative materials are used in developing
design values. Anchor bolt materials used are ASTM A
A307 (Grade B), A325, A449 and A687. Concret
assumed to have a minimum compressive strength (fc3,000 psi. Anchor bolts are heavy hex bolts or threaded
bars with one heavy hex nut placed in concrete. Bolt thr
at the embedded end of each threaded steel bar are sta
at two places below the heavy hex nut. All bolts are bro
to a snug tight condition as defined by AISC4 to en
good contact between attachments. The concrete is at lea
days old prior to tightening the anchor bolts in orde
prevent bolt rotation. Anchor bolts are designed for comb
shear and tension loads; the area of steel required for ten
and shear is considered additive. Criteria will be prese
such that either Working Stress Design (WSD) or Ultim
Strength Design (USD) may be used.
COMBINED TENSION AND SHEAR
Many authors have presented data and interaction equat
to account for the combined effects of tension and shear
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Fig. 1. Example of base plate loading
see Refs. 1, 3, 12, 14, 15 and 17). In this paper, the total
equired area of anchor bolt steel to resist tension and shear
oads is considered to be additive (see Appendix B, and Figs.
and 9).
Fig. 2. Effective stress area for limited depth(Ae)
Table 1A. Standard Anchor Bolt Basic Types
Type Description
Bolt
Spacing
r
Edge
Distance
m Commen
A Isola ted rrm mmv mv> rm/2,mv>
mt
B Shear reinforcement
onlyrrm rm/2 < m mt
C Shear reinforcement
plus overlapping
failure cones
r< rm mt< m< mv mt< rm/2
D Tension lap w/
reinforcement
r< rm mt < m 4 ' Note that Up must be greater than or equal to the
minimum specified tensile strength (FuAt) of the
standard anchor bolt as tabulated in Table 3. If Upis
less than FuAt, continue to increase the bolt
embedment depth until a solution is obtained.
The tensile strength of the concrete failure cone in aslab or wall is limited by the thickness of concrete
and the out-to-out dimensions of the anchors. I
degree lines extending from the exterior bolt h
toward the compression face do not intersect w
the concrete, then the effective stress area is lim
as shown in Fig. 2.
Type D Anchor BoltsAnchor bolts are classified as T
D, or tension lap with reinforcement, when all the follow
apply:
The closest bolt spacing (r) is less than rm.
The closest edge distance (m) is greater than or eto mtand less than rm/2.
The required bolt embedment depth is greater thaequal toLd.
The projected area of the overlapping conctensile stress cones (Ae) are extremely limited,
that failure mechanism is controlled by the reinfo
section rather than by the yielding of the anchor
steel. Such situations commonly arise in conc
piers.
The size of Type D anchor bolts is selected as per Typ
anchor bolts. Shear reinforcement is provided as per Typ
anchor bolts. Additional tension reinforcement is provide
follows:
Additional tension reinforcement is providedconcentrically located reinforcing steel (Ast),
that the anchor bolts are developed for
anchorage. Refer to Fig. 4 for the recommen
tension reinforcement practice.
The total area of tension reinforcement (Astdetermined by the following equation is develope
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Fig. 4. Tension lap
both sides of the critical plane of potential failure:
Ast= nFuAt/Fy
where
n= total number of bolts in the bolt group
Fy= minimum yield strength of reinforcing steel
NUMERICAL EXAMPLES
The application of the criteria presented in this paper is
llustrated by the following three example problems. The
xamples demonstrate Type A and D anchor bolts. An
xample is also presented for a column base plate for which
pecial attention is given to concrete strength and anchor bolt
ead placement.
Example 1: Type A (Isolated Bolt), see Fig. 5
Design Data:
TVF
i
== + +35
15kipskips
DL LL WL
f c' = 3000 psiSIF SIF = = =133 1 0 75. ; / .
= 0.55 (working stress design)
C= 1.85 (grouted base plate)
Fig. 5. Example 1: Type A anchor bolt
Design:
TCV Ti F=
+
=
+
=
185 15 35
0550 75 86
. ( )
.. kips
Refer to Table 2A and select 1 3 8 -in. dia. A325 bolts:
AtFy= 93.6 kips > 86 kips
Use 1 3 8 -in. dia. A325 bolts; rm= 33 in. and Ld= 24 in.
Example 2: Type D (Bolts in a Confined Pier),
see Figs. 6 and 7
Design Data:
Design anchor bolts for cylindrical heater foundation.
For empty + wind load combination:
TF= 1 kip; Vi= 3 kips
Fy= 60 ksi; fc= 3000 psi
SIF= 1.0; = 1.0r= 12; m= 4
= 0.55 (working stress design)C= 1.85 (grouted base plate)
Design:
TCV Ti f=
+
+
=
185 3 1
0 55119
. ( )
.. kips
From Table 2A, for -in. dia. A307 anchor bolt:
AtFy= 12.02 kips 11.9 kipsr= 12 in. rm= 12 in.
mtm< mv,where mt= 4 in.
Ld= 9 in.FuAt= 19,370 lbs (see Table 3)
Af A
fe
ut t
c
( ),
( . )required = =
4
19 370
4 0 65 3000 '
= 136 sq. in.
Ae= 102= 100 sq. in. < 136 sq. in. n.g.
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Fig. 6. Example 2: Type D anchor bolt
ncrease pier size to 24 in. square, (to avoid placement of
ension reinforcement), such that:
Ae= 122
= 144 sq. in. > 136 sq. in. o.k.Next, check the reinforced section and provide tension lap
einforcement.
Fig. 7. Example 2: Pier for Type D anchor bolt
Thus, we have a Type D anchor bolt.
AnF A
Fst
u t
y
= =4 1937
60
( . )
( )
= 1.29 sq. in. < 1.60 sq. in. (8-#4 bars)
Use 4-#4 U-bars.
Shear reinforcement must also be provided.
AF A
CFsv
u t
y
==
cos
.
( . )( )(. )45
1937
185 60 707
= 0.25 sq. in. < 0.40 sq. in. (1-#4 U-bar)
Use: 1-#4 U-bar in each direction.
Example 3: (See Figs. 8 and 9)
Design:
Ae r2= (28)
2= 2463 in.
2
U f A F Ap c e u t= 4 '
= 4 (.85) 4000 (2463) = 529,630 lbs
FuAt= 110,200(4) = 440,600 lbs < 529,630 lbs (see Tabl
Fig. 8. Example 3: Column base plate
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Fig. 9. Example 3: Interaction curves
Fig. 10. Projected area of heavy hexagonal head
Therefore, 4-1-in. maximum diameter bolts may be use
Note: Ld= 24 in. not adequate if fc= 3000 psi and = 0
i.e., anchor bolt head withinfar face reinforcement.
A F TCV T
t yi F =+
T= AtFy= 0.55AtFy= CVi+ Tf
C= 1.85, = 1.0
= 0.55(WSD)
T= AtFy(Table 2A)
Anchor Bolt Working Stress Loads:See Fig. 9 for plot.
A307
Bolt Dia.
(in.) 0.55AtFy Vi TF
2.82 0 2.82
1.52 01 12.00 0 12.0
6.49 0
1 27.82 0 27.8
15.04 0
1 37.62 0 37.6
20.34 0
NOMENCLATURE
Ae = Effective projected stress area to whichallowable uniform concrete tensile stres
applied to determine the pullout strengt
concrete
Ast = Total area of reinforcing steel acros
potential tension failure plane(s)
Asv = Total area of reinforcing steel acros
potential shear failure plane(s)
At = Tensile stress area of anchorage per AISC4
C = Shear coefficient applied to standard anc
which accounts for effects of various s
failure surfaces
= 1.10 when steel plates are embedded exposed surface flush with concrete surface
= 1.25 when steel plates are recessed in g
with bottom of plate in concrete surface
= 1.85 when steel plates are supported on g
mortar with exposed surface exterior
concrete surface
c = Equivalent circle for hex head
d = Nominal diameter of a bolt or plain bar
fc = Specified compressive strength of concrete
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3. Lee, D. W. and J. E. Breen Factors Affecting Anchor Bolt
Development Research Report 88-1F, Project 3-5-65-88,
Cooperative Highway Research Program with Texas Highway
Department and U.S. Bureau of Public Roads, Center for
Highway Research, University of Texas, Austin, Aug. 1966.
4. McMackin, P., R. Slutter and J. Fisher Headed Steel Anchors
Under Combined Loading Engineering Journal, American
Institute of Steel Construction, Vol. 10, No. 2, 1973.
5. PCI Design HandbookPrecast Prestressed Concrete Second
Edition, 1974.
6. Swirsky, R. A. et alLateral Resistance of Anchor Bolts Installed
in Concrete California Department of Transportation,
Sacramento, U.S. Department of Commerce National Technical
Information Service PB80-116189, May 1979.
7. TVA Anchorage to Concrete Tennessee Valley Authority
Division of Engineering Design, Thermal Power Engineering
Report No. CEB 75-32, Dec. 1, 1975.
APPENDIX A.
MINIMUM SPACING AND EMBEDMENT
An equivalent circle is assumed equal to the projected area of
heavy hexagonal head (see Fig. 10).
A F Fhex =
=3
2 08662 2
.
A Ccircle =2 4/
0866 42 2. /F C=
CF
F= =0866 4
1052. ( )
.
Tensile stress areaAe=A1A2= (L+ C/2)
2 (C/2)2
= [L2+ CL+ C
2/4 C
2/4]
= [L2+ CL]
Up= Ae[4 f c' (assume = 0.65)
= [L2+ CL][4(0.65) 3000 ]
= [L2+ CL]142
= 447 (L2+ CL)
Also, Up= FuAt,in pounds (see Table 3).Therefore,
0 = 447.4L2+ 447.4CL FuAt
0 = L2+ CL (FuAt/447.4)
L
C CF Au t
= +
2 4
447
2
=
CF A
Cu t2
112
2
+
See Table 4 for tabulated values. The design criteria ar
follows:
1. Minimum spacing of bolts (rm):
For A307: 2 8.0d= 16d
For A325/A449: 2 12.0d= 24d
For A687: 2 14.0d= 28d
Table 4. Tabulated Values of L
Heavy
Hex
Tensile Width
Bolt Stress Across Eff.
Diameter Area Flats Dia. A36,A307 A325,A449 A687
d At F C L L L
(in.) (in.2) (in.) (in.) (in.) *L/d (in.) *L/d (in.) *L/d
0.142 0.875 0.92 3.9 7.8 5.8 11.6 6.5 12.95
8 0.226
0.334 1.25 1.32 6.0 8.0 8.9 11.9 10.0 13.37
8 0.462
1 0.606 1.625 1.71 8.1 8.1 12.0 12.0 13.4 13.4
1 0.969
1 1.41 2.375 2.50 12.4 8.3 17.0 11.4 20.5 13.6
1 1.90
2 2.50 3.125 3.28 16.5 8.3 22.7 11.4 27.3 13.7
2 3.252 4.00 3.875 4.07 20.9 8.4 28.7 11.5 34.6 13.8
2 4.93
3 5.97 4.625 4.86 25.5 8.5 35.1 11.7 42.3 14.1
To ensure ductile failure, use the value ofL/d obtained by multiplying the largestL/d value in each column by an arbitrary factor of saf
1.33:
For A36, A307:L/d= 1.33 (8.5) = 12
For A325, A449:L/d= 1.33 (12.0) = 16
For A687:L/d= 1.33 (14.1) = 19
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2. Formula for embedment length (Ld):
L df
du= 12
58000, whereFuis in ksi
3. Embedment length (Ld):
For A307:Ld= 12d
For A325/A449:Ld= 17d
For A687:Ld= 19d
4. Values are tabulated in Table 2.
APPENDIX B. BOLT TENSION/
SHEAR INTERACTION EQUATIONS
The area of steel required for tension and shear is considered
dditive.
ACV
Fv
v
= =
area of steel required for shear
AT
FT
F
A
= =
area of steel required for tension
where
Fv = allowable shear stress
FA = allowable tension stress
= Probability factor (PF) or reciprocal of the stressincrease factor (1/SIF).
Note: 1.0.Av+ AT= At
whereAt= tensile stress area of anchorage
CV
F
TF
FA
v A
t+ =
CV
F A
T
F Av t
F
A t
+ =1
The shear force (V) causes a crushing/bearing failure near
he surface and translates the shear load into an effective
ension load in the anchorage.
Fv= FA
FvAt= FAAt= T
CV
T
T
T
F
+ =
1
TCV TF=
+
Note thatATmay be solved for as follows:
CV
F
T
FA
v
F
A
t+ =
Fv= FA= Fy
ACV T
Ft
F
y
=+
Expressed as an interaction equation:
CV
F A
F
F Ay t y t +
1
APPENDIX C. PROBABILITY-
BASED LIMIT STATES DESIGN (PBLSD)
1. The PBLSD design criterion is expressed in general fo
follows:
Design Resistance
Effect of Design Loads
In equation form: R Qe k kk
j
=
1
where
= resistance factor, less than 1.0, account
uncertainties in material strength
R = nominal design resistance (capacity), e
to the plastic strength of a struc
member
e = analysis factork = load factor, normally greater than 1.0, a
provides for load variationsQk= nominal design load effect
==k
j
1
e combined load effects from various causesdenotes th
2. The PBLSD uses the concept of limit state de
The nominal resistance (R) is always related
specific limit state. Two classes of limit states
pertinent to structural design: the ultimate
state and the serviceability or working limit st
Violation of the ultimate limit state involves lo
all or parts of the structure mechan
Serviceability limit state involves excesdeflection, excessive vibration and gross yielding.
3. The anchor bolt design equation expressed in PB
form may be derived as follows:
R Qe k kk
j
=
1
LetR= FyAt
where
Fy= minimum yield strength of steel
At= bolt tensile area
Let e= Let k k
k
j
i FQ CV T = = +
1
(the combined effect of tension and shear l
as derived in Appendix B.)
where
C= Shear coefficient
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Vi= 1V1+ 2V2+ ... kVkTF= 1T1+ 2T2+ ... kTk1= Load factor for load case number 12= Load factor for load case number 2
By substitution: FyAt[CVi+ TF]
F ACV T
Ty ti F+
=
whereFyAtvalues are tabulated in Table 2A.
Note: = 0.90 is a resistance factor which
accounts for uncertainties in
material strength (USD).
= 0.55 is a resistance factor which
converts the yield capacity to
working loads (WSD)
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